Page 195 - Aerodynamics for Engineering Students

178 Aerodynamics for Engineering Students

The lift per unit span

= apU2clT(l +cosO)dO = 7i-apU2c

It therefore follows that for unit span
I
CL = (4.31)
($q) =27ra

The moment about the leading edge per unit span
MLE = -lCp
dx

Changing the sign

Therefore for unit span

- 7i- (4.32)
-
Comparing Eqns (4.31) and (4.32) shows that

CL
CMLB = -- (4.33)
4
The centre of pressure coeficient kcp is given for small angles of incidence approxi-
mately by

(4.34)

and this shows a fixed centre of pressure coincident with the aerodynamic centre as is
necessarily true for any symmetrical section.

4.4.2 The general thin aerofoil section
In general, the camber line can be any function of x (or 0) provided that yc = 0 at
x = 0 and c (i.e. at 6 = 0 and T). When trigonometric functions are involved
a convenient way to express an arbitrary function is to use a Fourier series. Accord-
ingly, the slope of the camber line appearing in Eqn (4.22) can be expressed in terms
of a Fourier cosine series

(4.35)